**STAT 330: 96-3
**

Midterm, 18 October 1996Instructor: Richard Lockhart

**Instructions:** This is an open book test.
You may use notes, text, other books
and a calculator. Your presentations of statistical analysis will be
marked for clarity of explanation. I expect you to explain what
assumptions you are making and to comment if those assumptions seem
unreasonable. The exam is out of 25.

- A simple random sample of 900 adult British Columbians is
drawn. Each is asked how much beer he or she drinks per day.
- Assume that the 900 answers average 600 ml with a standard deviation of 750 ml. Give a 90% confidence interval for the average daily beer consumption of all adult British Columbians. [5 marks]
- Suppose that a year earlier a survey of 1600 voters had given an average of 550 ml with a standard deviation of 800 ml. Has daily beer consumption increased over the year? [5 marks]
- In the more recent survey (the one of 900 people) 300 report not drinking anything while in the earlier survey the corresponding figure was 400 people. Has there been a change in the fraction of all adults who do not drink? [5 marks]
- Briefly (2 or 3 sentences) criticize the assumptions used
in the previous three parts and comment on the realism of the
description of outcome of the survey. [1 mark]

- When you toss a thumbtack it can either land point up or tipped over. I have been told that the probability of landing point up is around 0.7 for a certain brand of tack. How many times should I toss the tack to be 99% sure that I will reject the hypothesis that the probability of landing point up is 0.5 at the level 5%? [3 marks]
- You have a sample from the density
for
*x*> 1 and for . Find the MLE of . [3 marks] - Suppose you have two independent samples, and
from two populations with means and
and variances and . Let and
be the two sample variances. Under the assumption that
I showed in class that is an unbiased estimate
of .
The variance of is
Show that
is an unbiased estimate of this variance and calculate the bias
of
(as an estimate of this )
if we do
*not*assume that . [3 marks]

Wed Feb 11 10:38:12 PST 1998